UBC Theses and Dissertations
Relationships between classroom processes and student performance in mathematics : an analysis of cross-sectional data from the 1985 provincial Assessment of Mathematics Taylor, Alan Richard
The purpose of this investigation was to examine, through the use of survey data, relationships between inputs of schooling and outcomes, as measured by student achievement in mathematics. The inputs of schooling were comprised of a number of variables grouped under each of the following categories: students' and teachers' backgrounds; students' and teachers' perceptions of mathematics; classroom organization and problem-solving processes. Outcome measures included student achievement on test total, problem solving and applications. A related question involved exploration of the appropriateness of using cross-sectional survey data to make decisions based on the relationships found among the input and output variables. To address this question, results from a subsequent longitudinal study, which utilized the same instruments, were examined first with post-test data and second with the inclusion of pre-test data as covariates. Data collected from teachers and students of Grade 7 in the 1985 British Columbia Assessment of Mathematics were re-analysed in order to link responses to Teacher Questionnaires with the students' results in teachers' respective classrooms. Responses were received from students in 1816 classrooms across the province and from 1073 teachers of Grade 7 mathematics. The data underwent several stages of analysis. Following the numerical coding of variables and the aggregation of student data to class level, Pearson product-moment correlations were calculated between pairs of variables. Factor analysis and multiple regression techniques were utilized at subsequent stages of the analysis. A number of significant relationships were found between teacher and student behaviors, and student achievement. Among the variables found to be most strongly related to achievement were teachers' attitudes toward problem solving, the number and variety of approaches and methods used by teachers, student perceptions of mathematics, and socio-economic status. Results also show that student background, students' and teachers' perceptions of mathematics, classroom organization and problem-solving processes all account for measurable variances in student achievement. The amount of variance accounted for, however, was higher for achievement on application items, measuring lower cognitive levels of behavior, than on problem-solving items which measured cognitive behavior at the critical thinking level. Through examination of the standardized beta weights from the cross-sectional and longitudinal models, it was found that prediction of change in achievement based on corresponding change in classroom process variables was similar for both models. Differences, however, were found for variables in the other categories.